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maksim [4K]
2 years ago
10

Quadrilateral RUST has a vertex at R(2, 4).

Mathematics
1 answer:
svetoff [14.1K]2 years ago
3 0

Given:

The coordinate of point R in quadrilateral RUST are (2,4).

R is dilated by a scale factor of 3, centered at the origin, followed by the translation (x, y)\to (x+4,y).

To find:

The coordinates of R' after dilation and translation.

Solution:

If a figure is dilated by a scale factor of 3, centered at the origin, then

(x,y)\to (3x,3y)

We value R(2,4).

R(2,4)\to R_1(3(2),3(4))

R(2,4)\to R_1(6,12)

The rule of translation is:

(x, y)\to (x+4,y)

Using this rule, we get

R_1(6,12)\to R'(6+4,12)

R_1(6,12)\to R'(10,12)

Therefore, the coordinates of point R' are (10,12) and the correct option is B.

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<u>Question 1</u>

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<u>Question 2</u>

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<u>Question 3</u>

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<u>Formula used</u>

Volume of a prism = base area × height

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<h3><u>Question 1</u></h3>

⇒ Volume of Figure A = (5 · 7)(2)

                                     = 70 cm³

⇒ Volume of Figure B = (13 · 7)(2)

                                     = 182 cm³

⇒ Total Volume = Volume of Figure A + Volume of Figure B

                           = 70 + 182

                           = 252 cm³

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<u>Rewritten statement</u>:

The volume of figure A can be found by multiplying (5 · 7)(2).

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<h3><u>Question 2</u></h3>

⇒ Volume of rectangular prism = (15 · 15)(2)

                                                    = 450 mm³

⇒ Volume of central cube = 2³

                                            = (2 · 2 · 2)

                                            = 8 mm³

⇒ Total Volume = Volume of rectangular prism - Volume of cube

                           = 450 - 8

                           = 442 mm³

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<u>Rewritten statement</u>:

The total volume of the figure is 442 mm³

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<h3><u>Question 3</u></h3>

⇒ Volume of rectangular prism = (12 · 3)(8)

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⇒ Volume of triangular prism = (1/2 · 12 · 6)(3)

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⇒ Total Volume = Volume of rectangular prism + Volume of triangular prism

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<u>Rewritten statement</u>:

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